OK, I am an Otaku (not a radical otaku, but a serious collector of anime, film, and anime merchandise). I have enjoyed animated film since I was a kid. I will post a few things about me here...you decide if I am a "baby," OK?
I am 59 years old.
I have MA and Ph.D. degrees in Clinical Psychology.
I have a Master of Public Administration degree.
I am an Intermediate level Japanese Language Learner.
I retired at 55 from a career as a Psychologist and Counselor.
I am married to a Psychiatrist. (...who worked her way through Medical School by doing freelance animation and editing for a major anime production company.)
Last year at Halloween, my wife and I held a cosplay party.
Now, if that qualifies me as a "baby," I am going to stay a "baby" for the rest of my life.
Who cares if it is cool or not? I also collect model trains...is that cool or uncool? Neil Young and Bruce Springsteen both think it is "cool." Neil Young is even a part owner of Lionel Trains.

AND, one of the biggest anime fans (especially Evangelion) is the comedian Robin Williams...is he cool?
Just enjoy what you enjoy...and don't let others run a "mind game" on you. If you like anime, watch it and enjoy it.
Here are some of my favorite anime:
Grave of the Fireflies (one of the best films ever made)
Ah! My Goddess
Azumanga Daioh
Evangelion (a very serious psychological post-apocalyptic series)
Akira
Elfen Lied (not for folks your age...sorry, it is NC-17)
Aishiteruze Baby
FLCL (Fooly Cooly)
Chobits